Theory of current-voltage instabilities in superlattices

The theory of the uniform electric-field distribution instability in superlattices is developed. The instability with respect to high-field domain formation was discovered some time ago by Esaki and Chang but no microscopic theory has been proposed so far. To determine the instability condition we consider first the conductivity of a superlattice with a uniform electric-field distribution for arbitrary relations between the width of the miniband, the electric potential drop per period, and the energy uncertainty due to scattering. Such a general case can be described quantitatively with the help of the density matrix if an effective electron temperature is larger than those three characteristic energies. The instability threshold corresponds to an electric field for which the separation between Stark levels in the superlattice becomes larger than the energy uncertainty due to scattering. The physical reason for the instability is that any local increase of the field leads to a larger separation between the Stark levels and to the local decrease of the current. The solution of the instability problems shows that near the instability threshold only long-wavelength fluctuations are unstable. At the initial stage of the development of the instability nonlinear effects accelerate the fluctuation growth.